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17.2 Properties of Mechanical Waves
A surfer needs to understand the properties of waves.
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17.2 Properties of Mechanical Waves
What determines the frequency of a wave?
Any periodic motion has a frequency, which is the number of complete cycles in a given time.
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17.2 Properties of Mechanical Waves
Any motion that repeats at regular time intervals is called periodic motion.
• The time required for one cycle is called the period.
• Frequency is the number of complete cycles in a given time.
• Frequency is measured in cycles per second, or hertz (Hz).
Frequency and Period
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17.2 Properties of Mechanical Waves
A. A wave vibrating at one cycle per second has a frequency of 1.0 Hz.
B. A wave vibrating at two cycles per second has a frequency of 2.0 Hz.
Frequency and PeriodFrequency = 1.0 hertzOne cycle per second
Frequency = 2.0 hertzTwo cycles per second
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17.2 Properties of Mechanical Waves
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17.2 Properties of Mechanical Waves
For a transverse wave, wavelength is measured between adjacent crests or between adjacent troughs.
For a longitudinal wave, wavelength is the distance between adjacent compressions or rarefactions.
Wavelength
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17.2 Properties of Mechanical Waves
Wavelength can be measured from any point on a wave to the same point on the next cycle of the wave.
Wavelength
Long wavelength Short wavelength
Rest position
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17.2 Properties of Mechanical Waves
When the wavelength is in meters, and the frequency is in hertz, the units for speed are meters per second.
The speed of a wave is also calculated by dividing its wavelength by its period.
Wave Speed
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17.2 Properties of Mechanical Waves
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17.2 Properties of Mechanical Waves
Speed of Mechanical Waves
One end of a rope is vibrated to produce a wave with a wavelength of 0.25 meter. The frequency of the wave is 3.0 hertz. What is the speed of the wave?
Wave Speed
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17.2 Properties of Mechanical Waves
Read and UnderstandWhat information are you given?
Wave Speed
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17.2 Properties of Mechanical Waves
Read and UnderstandWhat information are you given?
Wave Speed
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17.2 Properties of Mechanical Waves
Plan and Solve
What unknown are you trying to calculate?
What formula contains the given quantities and the unknown?
Wave Speed
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17.2 Properties of Mechanical Waves
Plan and Solve
What unknown are you trying to calculate?
What formula contains the given quantities and the unknown?
Wave Speed
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17.2 Properties of Mechanical Waves
Plan and Solve
Replace each variable with its known value.
Wave Speed
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17.2 Properties of Mechanical Waves
Plan and Solve
Replace each variable with its known value.
Wave Speed
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17.2 Properties of Mechanical Waves
Look Back and CheckIs your answer reasonable?
Wave Speed
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17.2 Properties of Mechanical Waves
Look Back and CheckIs your answer reasonable?
Because the frequency is 3.0 hertz, the wave should travel a distance of 3 wavelengths in 1 second. This distance is 0.75 meters, which agrees with the calculated speed of 0.75 m/s.
Wave Speed
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17.2 Properties of Mechanical Waves
1. A wave on a rope has a wavelength of 2.0 m and a frequency of 2.0 Hz. What is the speed of the wave?
Answer:
Wave Speed
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17.2 Properties of Mechanical Waves
1. A wave on a rope has a wavelength of 2.0 m and a frequency of 2.0 Hz. What is the speed of the wave?
Answer:
The speed is 2.0 m × 2.0 Hz = 4.0 m/s
Wave Speed
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17.2 Properties of Mechanical Waves
2. A motorboat is tied to a dock with its motor running. The spinning propeller makes a surface wave in the water with a frequency of 4 Hz and a wavelength of 0.1 m. What is the speed of the wave?
Answer:
Wave Speed
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17.2 Properties of Mechanical Waves
2. A motorboat is tied to a dock with its motor running. The spinning propeller makes a surface wave in the water with a frequency of 4 Hz and a wavelength of 0.1 m. What is the speed of the wave?
Answer:
The speed is 0.1 m × 4 Hz = 0.4 m/s
Wave Speed
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17.2 Properties of Mechanical Waves
3. What is the speed of a wave in a spring if it has a wavelength of 10 cm and a period of 0.2 s?
Answer:
Wave Speed
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17.2 Properties of Mechanical Waves
3. What is the speed of a wave in a spring if it has a wavelength of 10 cm and a period of 0.2 s?
Answer:
The speed is 10 cm/0.2 s = 50 cm/s
Wave Speed
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17.2 Properties of Mechanical Waves
4. What is the wavelength of an earthquake wave if it has a speed of 5 km/s and a frequency of 10 Hz?
Answer:
Wave Speed
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17.2 Properties of Mechanical Waves
4. What is the wavelength of an earthquake wave if it has a speed of 5 km/s and a frequency of 10 Hz?
Answer:
The wavelength is (5 km/s)/10 Hz = 0.5 km.
Wave Speed
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17.2 Properties of Mechanical Waves
The speed of a wave can change if it enters a new medium, or if variables such as pressure and temperature change.
For many kinds of waves, the speed of the waves is roughly constant for a range of different frequencies.
The wave with the lower frequency has a longer wavelength.
Wave Speed
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17.2 Properties of Mechanical Waves
Amplitude
How is the amplitude of a wave related to the wave’s energy?
The amplitude of a wave is the maximum displacement of the medium from its rest position.
The more energy a wave has, the greater is its amplitude.
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17.2 Properties of Mechanical Waves
The amplitude of a transverse wave is the distance from the rest position to a crest or a trough.
It takes more energy to produce a wave with higher crests and deeper troughs.
Amplitude
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17.2 Properties of Mechanical Waves
The more energy a wave has, the greater is its amplitude.
Amplitude
Rest position
High amplitude
Low amplitude
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17.2 Properties of Mechanical Waves
The amplitude of a longitudinal wave is the maximum displacement of a point from its rest position.
The more energy the wave has, the more the medium will be compressed or displaced.
Amplitude
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17.2 Properties of Mechanical Waves
Assessment Questions
1. While wading in shallow waters, six waves crash into your legs in a 24-second span. What is the frequency of the waves? a. 4 Hz
b. 18 Hz
c. 0.25 Hz
d. 2 Hz
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17.2 Properties of Mechanical Waves
Assessment Questions
1. While wading in shallow waters, six waves crash into your legs in a 24-second span. What is the frequency of the waves? a. 4 Hz
b. 18 Hz
c. 0.25 Hz
d. 2 Hz
ANS: C
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17.2 Properties of Mechanical Waves
Assessment Questions
2. What is the speed of an earthquake wave if it has a wavelength of 2.3 km and a frequency of 3 Hz?a. 6.9 kmb. 5.3 kmc. 6.0 kmd. 1.3 km
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17.2 Properties of Mechanical Waves
Assessment Questions
2. What is the speed of an earthquake wave if it has a wavelength of 2.3 km and a frequency of 3 Hz?a. 6.9 kmb. 5.3 kmc. 6.0 kmd. 1.3 km
ANS: B
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17.2 Properties of Mechanical Waves
Assessment Questions
3. Which wave property increases as the energy of a wave increases? a. period
b. frequency
c. wavelength
d. amplitude
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17.2 Properties of Mechanical Waves
Assessment Questions
3. Which wave property increases as the energy of a wave increases? a. period
b. frequency
c. wavelength
d. amplitude
ANS: D